How can I avoid or clean distortion in curves imported from SVG?
As explained in How can I model Gothic style windows? (credit to ardito comment)

You don't actually need to separate the board and then curve it, instead:


open the SVG in InkScape and change the image to be filled (instead of only stroke)
import the SVG to blender 
select the important mesh and do Alt+C and turn it into a mesh
now you can simply extrude it and create a 3D object with carved spaces.



Note: if the curve is distorted then select it, in the Properties editor in the Object Data tab, on the right, find Extrude and increase it by 1.